Problem: The following line passes through point $(8, -7)$ : $y = -\dfrac{6}{5} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(8, -7)$ into the equation gives: $-7 = -\dfrac{6}{5} \cdot 8 + b$ $-7 = -\dfrac{48}{5} + b$ $b = -7 + \dfrac{48}{5}$ $b = \dfrac{13}{5}$ Plugging in $\dfrac{13}{5}$ for $b$, we get $y = -\dfrac{6}{5} x + \dfrac{13}{5}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(8, -7)$